Anyone who follows the history of the NCAA tournament should know this is an inherently difficult exercise. Higher seeds win 71 percent of the time as the bracket shrinks from 68 teams to one. But the top teams do exit, and often when they do, it’s because a critical shortcoming in their statistical profile was exploited by a uniquely talented lower seed.

The goal here is to spot the top seeds particularly prone to toppling before they’re supposed to based on seed (No. 1 seeds should reach the Final Four, No. 2s the Elite Eight, No. 3s the Sweet 16, etc.). We’ve identified 10 teams so precariously perched over the past three NCAA tournaments. Seven of those 10 fell before their seed said they should (Villanova and Kansas in 2015; Oregon, Xavier and Utah in 2016; Florida State and Kansas in 2017).

Identifying such upsets early can have massive value if you’re in a highly competitive pool, both in making risky (if slightly better informed) upset picks, but also in deciding whom to back all the way to the title. So while the top seeds may have the odds in their favor, March is mad for a reason, and these are our candidates to add to the insanity with an untimely loss.

No. 1 Xavier

The Musketeers are, by far, the most over-seeded No. 1 according to Ken Pomeroy’s metrics, profiling closer to a No. 4 seed. In fact, Pomeroy’s metrics rank two teams seeded No. 4 or worse in the bracket ahead of Xavier — and one happens to be in the same half of the West bracket as the Musketeers.

That would be Gonzaga, an adept offensive team well-suited to take advantage of Xavier’s deficiencies on defense. The Musketeers rank a mediocre 180th against two-point shooting, while the Bulldogs are the fifth-best team in the nation at scoring inside the arc. Moreover, Xavier doesn’t generate turnovers defensively (318th in the nation) and, if Gonzaga has time to work the ball against that defense, it could be bad news for Xavier.

Xavier also relies quite a bit on free throws to score points. On one hand, that’s efficient. On the other, it requires opponents to commit fouls and for referees to call them. The Zags are pretty adept at playing defense without putting foes on the foul line, and if they can do so against Xavier, an upset wouldn’t be a surprise.

No. 1 Kansas

This comes down to one big red flag in an otherwise strong statistical profile. The Jayhawks allow a lot of offensive rebounds. Like, 297th-out-of-351-teams-in-defensive-rebounding-percentage a lot. This is particularly problematic given a potential second-round matchup against Seton Hall and human glass cleaner Angel Delgado who, along with Michigan State’s Nick Ward, is one of the best offensive rebounders in the tournament.

Kansas wouldn’t see Ward and the Spartans until a potential Elite Eight matchup, but getting the Pirates in the second round would stink for the Jayhawks. Of course, the alternative isn’t that much better. Seton Hall’s first-round foe, North Carolina State, ranks 37th nationally in offensive rebounding percentage, comparable to Seton Hall (29th). Auburn, a potential Sweet 16 opponent, is also in the top 50. And a regional final matchup against the Spartans, the fifth-best team in the nation on the offensive glass, should be flat-out terrifying.

No. 2 Cincinnati

It’s nothing against the Queen City. Gimme that Skyline Chili five-way life and some Graeter’s ice cream for desert. Great meal, but it’ll leave a brick in your stomach. And speaking of bricks …

The biggest question the Bearcats need to answer to reach the Elite Eight: Can they score?

Mick Cronin’s crew is brutally efficient in its own end, posting numbers that would drop your jaw if it wasn’t already bound up like the rest of your body by the Bearcats’ defensive duct tape. Cincinnati contests shots and forces turnovers quite a bit (22.4 percent of possessions, ninth-best in the nation). That can be particularly crippling given the Bearcats’ slow pace of play, which limits possessions and provides foes precious few chances to score.

Offensively, though, the Bearcats are less than stellar. They’re middle of the pack in effective field goal percentage and downright bad at the line (68.8 percent, 274th in the nation). Their only truly standout statistical category is offensive rebounding, where they thrive (38.3 percent, third in the nation). That’s important, considering they don’t connect on many of their shot attempts.

The problematic matchups in the bracket? If Nevada gets by Texas, the Wolf Pack could be a tough out for the Bearcats. Nevada takes care of the ball, turning it over on just 13.9 percent of its possessions. The Wolf Pack also shoots well from three-point range at nearly 40 percent, ranking 21st in the nation. Cincinnati is great at defending the perimeter (ninth in three-point defense), but it’s even better inside (No. 2). In its four losses, Cincinnati has allowed foes to shoot 40 percent or better from deep. If there’s a good way to attack the Bearcats, it’s over the top.

Mike HumeMike Hume is the assignment editor for The Washington Post's NFL and NHL coverage at both national and local levels. He also manages coverage of fantasy football, e-sports and gaming, and oversees the Fancy Stats blog with Neil Greenberg. Follow